Analysis of two variables

[Catalin Mos]

Dear all,

I have a question regarding an analysis of two variables which capture the same phenomena (country level of enforcement).
One of the variable is developed by me and the other was frequently used in prior literature.
My objective is to show that for EU my proxy explain better the variation in dependent variable or to show that my variable is better.

Do you have any idea what type of analysis I could use to show this?

Thank you in advance!

[Carlo Lazzaro]

Catalin:
the main question is: better with respect to what? A dependent variable?
If that were the case, you may want to consider two regression models and compare their results (say, via Adjusted R_Sq, if your deoendent variable is a continuous one).

[Catalin Mos]

Dear Carlo,

Thank you for the response.
Yes, in relation with the dependent variable.
My initial thoughts was to standardize the two variables and to introduce both of them in one regression and to analyze the coefficients.
Do you think that this method is appropriate or I should go with your proposed method.

Thank you!

[Carlo Lazzaro]

Catalin:
you may run two simple regressiona (that is, regressions with one predictor ony) and then compare them via -estat ic-:

use "C:\Program Files\Stata17\ado\base\a\auto.dta"
. reg price mpg

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(1, 72)        =     20.26
       Model |   139449474         1   139449474   Prob > F        =    0.0000
    Residual |   495615923        72  6883554.48   R-squared       =    0.2196
-------------+----------------------------------   Adj R-squared   =    0.2087
       Total |   635065396        73  8699525.97   Root MSE        =    2623.7

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         mpg |  -238.8943   53.07669    -4.50   0.000    -344.7008   -133.0879
       _cons |   11253.06   1170.813     9.61   0.000     8919.088    13587.03
------------------------------------------------------------------------------

. estat ic

Akaike's information criterion and Bayesian information criterion

-----------------------------------------------------------------------------
       Model |          N   ll(null)  ll(model)      df        AIC        BIC
-------------+---------------------------------------------------------------
           . |         74  -695.7129  -686.5396       2   1377.079   1381.687
-----------------------------------------------------------------------------
Note: BIC uses N = number of observations. See [R] BIC note.

. reg price trunk

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(1, 72)        =      7.89
       Model |  62747229.9         1  62747229.9   Prob > F        =    0.0064
    Residual |   572318166        72  7948863.42   R-squared       =    0.0988
-------------+----------------------------------   Adj R-squared   =    0.0863
       Total |   635065396        73  8699525.97   Root MSE        =    2819.4

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       trunk |   216.7482   77.14554     2.81   0.006     62.96142     370.535
       _cons |   3183.504   1110.728     2.87   0.005     969.3088    5397.699
------------------------------------------------------------------------------

. estat ic

Akaike's information criterion and Bayesian information criterion

-----------------------------------------------------------------------------
       Model |          N   ll(null)  ll(model)      df        AIC        BIC
-------------+---------------------------------------------------------------
           . |         74  -695.7129  -691.8637       2   1387.727   1392.335
-----------------------------------------------------------------------------
Note: BIC uses N = number of observations. See [R] BIC note.

.

In this case, the first specification outperforms the second one, as AIC and BIC are both lower.
Obviously, simple regression models are easily misspecified (see -linktest-).